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5. Suppose the data concerning first-year salaries of graduates follows normal distribution with the population mean ? = $60, 000 and the stan- dard deviation ? = $10,000. Denote X as the salary of a randomly selected graduate.
(a)
What is the probability that X is greater than $40, 000?
(b)
What is the probability that X is between $30, 000 and $90, 000?
(c)
Suppose we interviewed 5 randomly selected SBU graduates
and their salaries are X1, X2, …, X5. Denote the average salaries
of these 5 people as X = X1+X2+X3+X4+X5 . What is the ex-5
pectation and the variance of X?
(Hint: Use the standard normal table to answer (a) and (b).)